Weak Lensing. Alan Heavens University of Edinburgh UK

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1 Weak Lensing Alan Heavens University of Edinburgh UK

2 Outline History Theory Observational status Systematics Prospects

3 Weak Gravitational Lensing Coherent distortion of background images Shear, Magnification, Amplification Jain & Seljak

4 Weak lensing: the Bush years 2000 First detections (Bacon et al, Kaiser et al, Wittman et al, van Waerbeke et al) Weak-lensing selected cluster catalogues (e.g. Miyazake et al, Wittman et al) Non-parametric mass distributions in clusters (e.g. Kneib et al, Clowe et al, Jee et al, Gray et al) Dark matter power spectrum (Brown et al, Heymans et al, Hoekstra et al, Semboloni et al) 2004 Bullet cluster challenge to MOND (Clowe et al) D potential reconstruction (Taylor et al, Massey et al) Evolution of structure (Bacon et al) D analyses (Heavens et al, Kitching et al, Taylor et al) sq deg surveys, with small error bars (Benjamin et al, Fu et al)

5 Physics Einstein gravity θ β Van Waerbeke & Mellier 2004 η γ 2 γ 1 e.g. Gunn 1967 (Feynman 1964); Kristian & Sachs 1966 Complex shear γ =γ 1 + i γ 2

6 E and B modes Lensing essentially produces only E modes Jain & Seljak B modes from galaxy clustering, 2 nd - order effects (both small), imperfect PSF modelling, optics systematics, intrinsic alignments of galaxies

7 Lensing potential Integrate: Lensing potential (Flat Universe) And convergence κ and shear are given by transverse derivatives of φ: Note: dependence is on gravitational potential: lensing probes the mass distribution directly. Bias is not an issue. Expected Shear is ~ 1%

8 Reconstruction of density/potential Halo profiles (Josh Frieman s talk) 2D cluster potential/density Hot Gas (X-ray) Dark Matter (Lensing) Galaxies 3D A901: Gray et al 2004 Markevitch et al 2002; Clowe et al 2004 COMBO-17: Taylor et al 2004 COSMOS: Massey et al 2007

9 Statistical analysis: 2D E.g. Shear-shear correlations on the sky Depends on how clumpy the Universe is: P(k,t) Peacock & Dodds 96; Smith et al 2003 Simulated: Jain et al 2000 How far away the galaxies are: n(z) To get n(z), best practical way is via photo-zs

10 Results: tension with WMAP? Early CFHTLS results σ 8 22 sq deg; median z=0.8 Hoekstra et al 2005; see also Semboloni et al 2005 Ω m σ 8 = at Ω m =0.26 BUT: n(z) estimated from Hubble Deep Field galaxies large sample variance

11 Reanalysis of recent data 100 square degree survey (Benjamin et al 2007) Better n(z) from photozs from same (CFHTLS deep) survey Reduced tension between lensing results and WMAP.

12 Recent results: CFHTLS E modes B modes 57 sq deg; median z=0.95 WMAP3 Fu et al 2008

13 Dark Energy: effects Distance-redshift relations r(z), D A,D L Growth rate of perturbations g(z) Z information is crucial

14 Steps to 3D: lensing in slices Dividing the source distribution improves parameter estimation Hu (1999)

15 Full 3D weak lensing Heavens 2003 Use individual photo-zs: Very noisy, point-process sampling of 3D shear field 3D shear power spectrum probes r(z) and g(z) Reduces tomography statistical errors by factor ~ 1.3

16 Shear Ratio Test The ratio of R( Ω V, Ω m, w) = shears has a γ ( z γ ( z 1 2, z, z L L ), ) purely geometric dependence R r( z = r( z 2 1 )[ r( z )[ r( z 1 2 ) ) r( z r( z L L )] )] γ 1 γ 2 Observer Galaxy cluster/lens z L Depends only on global geometry: Ω DE, Ω m and w. Apply to large signal from galaxy clusters Similar accuracy to 3D shear power spectrum (Jain & Taylor, 2003, Taylor et al 2007) z z 2 1

17 w from 3D lensing Proof of concept: COMBO-17 (0.75 square degrees) 3D shear Shear ratio w = -1.1 ± 0.6 Not a competitive error, but proof of concept for future large 3D surveys Predicted a priori Kitching et al 2007

18 Estimating shear Measure ellipticity of galaxy Estimate shear γ by averaging over many galaxies (since <e I >=0) Dispersion in e I is ~0.3 Shear is ~0.01

19 Image quality Telescope optics & atmosphere may distort images up to ~10% Use stars to correct for the Point Spread Function (PSF) distortions

20 Shape measurement Needs to be done without significant bias Examples: moments (KSB) orthogonal function decomposition (shapelets) shape fitting (im2shape, lensfit)

21 Requirements are stringent: Fit g = (1+m) g true + c Need m < 5-8 x 10-3 for shape measurement not to dominate errors on w in DUNE Lensfit (Miller et al 2007; Kitching et al 2008): m = (6 5) x 10-3 from simulated STEP (Heymans et al 2006) data Massey et al 2007

22 Astrophysical complications Lensing analysis assumed orientations of source galaxies are uncorrelated Intrinsic correlations destroy this Intrinsic alignments e I + g <e e*> = < gg*> + <e I e I *>

23 Intrinsic alignments <e e*> = < gg*> + <e I e I *> + < g e I * > + < e I g* > <e I e I *> Theory: Tidal torques Heavens, Refregier & Heymans 2000, Croft & Metzler 2000, Crittenden et al 2001 etc Brown et al 2000 Downweight/discard pairs at similar photometric redshifts (Heymans & Heavens 2002; King & Schneider 2002a,b) REMOVES EFFECT~COMPLETELY

24 Shear-intrinsic alignments < g e I * > Hirata & Seljak 2004 Tidal field contributes to weak shear (of background) Tidal field could also orient galaxies (locally) (Hirata and Seljak 2004; Mandelbaum et al 2005, Trujillo et al 2006, Yang et al 2006, Hirata et al 2007) SDSS: Mandelbaum et al 2005 Expect 5-10% contamination Simulations: Heymans et al 2006

25 Removing shear-intrinsic ellipticity contamination Expect signal to have different redshift dependence from weak lensing fl model it Heymans et al 2006; King 2006; Hirata & Seljak 2004 Hirata et al 2007

26 Photometric redshifts z true -z photometric z photometric Ú > 0.002, it is an important systematic for w for DUNE. Need to calibrate with many (~3 x 10 5 ) spectra (Abdalla et al 2007) Need good photo-zs to model and remove shear-intrinsic alignments (Bridle & King 2007) Reasonable priors suggest a degradation by a factor of ~2 in DUNE Figure of Merit (1/Dw 0 Dw a ) from systematics (Kitching et al 2008b) Abdalla et al 2007

27 Prospects w(a)=w 0 +w a (1-a) Chevallier & Polarski Ground: KIDS, Pan- STARRS 1, DES, HSC, LSST Space: DUNE,SNAP (see Anaïs Rassat s talk) Area/ sq deg Median z Gals/ sq min Start Date KIDS 1700 ~0.6 ~ PS ~0.65 > HSC 2000 > DUNE ~

28 Beyond-Einstein gravity Dynamic Dark Energy can mimic the H(z), r(z) of any modified gravity law Probing both r(z) and g(z) allows lifting of this degeneracy, at least for some classes of model (See Martin Kunz talk) Parametrise gravity by Minimal Modified Gravity law (Linder 2005) γ 0.55 (GR); γ 0.68 (Flat DGP model) Bayesian Evidence ratio 3.8 (2.8s) for Pan-STARRS 1, 63 (11s) for DUNE (Heavens et al 2007; Amendola et al 2007)

29 Conclusions Much progress since 2000: 1 Ø 10 2 Ø 10 4 sq deg Lensing in 3D is potentially very powerful: precision of ~1% on w potentially possible from ground. Needs: Large area (tens of thousands of square degrees) Depth z~1 Very small telescope distortions Good photometric redshifts Systematics: shape measurement, intrinsic alignments, photo-zs: probably reduce DUNE Figure of Merit by factor ~2 Next-generation surveys could further distinguish Dark Energy from Modified Gravity